Helical preconditioning and splines in tension
نویسنده
چکیده
Splines in tension are smooth interpolation surfaces whose behavior in unconstrained regions is controlled by the tension parameter. I show that such surfaces can be efficiently constructed with recursive filter preconditioning and introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.
منابع مشابه
The Wilson-Burg method of spectral factorization with application to helical filtering
Spectral factorization is a computational procedure for constructing minimumphase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging the terms. This procedure i...
متن کاملTENSION TRIGONOMETRIC SPLINES INTERPOLATION METHOD FOR SOLVING A LINEAR BOUNDARY VALUE PROBLEM
By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...
متن کاملPiecewise L-splines of order 4: Interpolation and L2 error bounds for splines in tension
Piecewise L-splines are generalizations of L-splines, in the sense that they satisfy different differential equations in different mesh intervals. Prenter attempted in [P.M. Prenter, Piecewise L-Splines, Numer. Math. 18 (2) (1971) 243–253] to obtain results on piecewise L-splines by generalizing the results of Schultz and Varga on L-splines in [M.H. Schultz, R.S. Varga, L-Splines, Numer. Math. ...
متن کاملOn Construction of Fourth Order Chebyshev Splines
It is an important fact that general families of Chebyshev and L-splines can be locally represented, i.e. there exists a basis of B-splines which spans the entire space. We develop a special technique to calculate with 4 order Chebyshev splines of minimum deficiency on nonuniform meshes, which leads to a numerically stable algorithm, at least in case one special Hermite interpolant can be const...
متن کاملRange restricted interpolation using Gregory’s rational cubic splines
The construction of range restricted univariate and bivariate interpolants to gridded data is considered. We apply Gregory’s rational cubic C splines as well as related rational quintic C splines. Assume that the lower and upper obstacles are compatible with the data set. Then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range rest...
متن کامل